# Zsigmondy’s theorem

For all positive integers $q>1$ and $n>1$, there exists a prime $p$ which divides ${q}^{n}-1$ but doesn’t divide ${q}^{m}-1$ for $$, except when $q={2}^{k}-1$ and $n=2$ or $q=2$ and $n=6$.

Title | Zsigmondy’s theorem |
---|---|

Canonical name | ZsigmondysTheorem |

Date of creation | 2013-03-22 13:10:44 |

Last modified on | 2013-03-22 13:10:44 |

Owner | lieven (1075) |

Last modified by | lieven (1075) |

Numerical id | 6 |

Author | lieven (1075) |

Entry type | Theorem |

Classification | msc 11A51 |

Synonym | Birkhoff-Vandiver theorem |